I'm sorry to hear about that kind of pressure in KS1, if these comments really are being said to such young children I would maybe refer it to headteacher if not done so already. I dont have a problem with KS1 SATs in the slightest - if and only if they are done in the right way. The good thing about KS1 SATs is that they are not the be all and end all, although they give a good reflection of the childs capabilities (usually) the final level is decided by the class teacher (with others moderating) who can take in account the whole child - so if they completly fall apart on the day teacher assessment can be used to give them the level they are capable of. The Boycott is largly around KS2 SATs as there is not this opportunity.
The national curriculum statement certainly isn't true. In fact one of the Year 2 learning objectives touch on children following thier own line of enquiry so I can only imagine this is developed further throughout the school years (apologies i'm KS1 trained.)
Relating back to the homework (sorry for hijack also haha) - I give my class spellings once a week, although may be seen as Rote learning they are linked to the weekly phonics lessons and it is really important (in order for it to support my teaching) that parents do help learn these.
However we also give them one other homework in the week that they can have a week, or 2/3 weeks depending to do - in which you set an open ended task in a book. For example design your own veichle (linking to D&T) - think about what you would need to make it etc. These books are intended to be open ended and the chn have ownership over how they complete them, so some may simple draw and label a veichle, some may write about it, some may make a model and bring it in to discuss, videos of themselves presenting thier idea, paintings - anything.
Since we started it the amount of children completing homework has risen as they are not restricted and for me - seeing how much effort and the amazing results some of these children are producing is fantastic.
The great thing about it is that as they are so open ended all children regardless of ability can access it and take it in thier own direction.
We do still drop in the odd numeracy/literacy/science sheet still if it is worthwhile - oop 
The only thing I would say is if you aren't going to do homework - definitly have a word with teacher. If I had a parent that had a problem with it then I would rather know so we could try and resolve situation. If it is something child is confident with then its sometimes useful for them to consolodate this in an environment outside of school.
Sorry for the huge message - time to get bits ready for my new little lot now.
xx